In lhis paper, we study the variable structure control of indefinite-dimensionalcontrol systems with the functional analysis method. The reaching conditions, stabilityconditions and the approximating conditions of sli...In lhis paper, we study the variable structure control of indefinite-dimensionalcontrol systems with the functional analysis method. The reaching conditions, stabilityconditions and the approximating conditions of sliding mode, as well as the generalform of the variable structure control law are given. and the elementary frame of thevariable structure control of indefinite-dimensional systems is built.展开更多
A method is proposed to deal with the uncertain multiple attribute group decision making problems,where 2-dimension uncertain linguistic variables(2DULVs)are used as the reliable way for the experts to express their f...A method is proposed to deal with the uncertain multiple attribute group decision making problems,where 2-dimension uncertain linguistic variables(2DULVs)are used as the reliable way for the experts to express their fuzzy subjective evaluation information.Firstly,in order to measure the 2DULVs more accurately,a new method is proposed to compare two 2DULVs,called a score function,while a new function is defined to measure the distance between two 2DULVs.Secondly,two optimization models are established to determine the weight of experts and attributes based on the new distance formula and a weighted average operator is used to determine the comprehensive evaluation value of each alternative.Then,a score function is used to determine the ranking of the alternatives.Finally,the effectiveness of the proposed method is proved by an illustrated example.展开更多
In practice, it is very difficult to find the solution of recurrence relation by using the characteristic roots. By applying iteration and induction we present an explicit formula of general solution for a class of ho...In practice, it is very difficult to find the solution of recurrence relation by using the characteristic roots. By applying iteration and induction we present an explicit formula of general solution for a class of homogeneous trinomial recurrence of variable coefficients with two indices. It provides a concrete and applicable model to solve the relevant problem with computer.展开更多
We study the high order equilibrium distributions of a counting random variable. Properties such as moments, the probability generating function, the stop--loss transform and the mean residual lifetime, are derived. E...We study the high order equilibrium distributions of a counting random variable. Properties such as moments, the probability generating function, the stop--loss transform and the mean residual lifetime, are derived. Expressions are obtained for higher order equilibrium distribution functions under mixtures and convolutions of a counting distribution. Recursive formulas for higher order equilibrium distribution functions of the (a,b,0) -family of distributions are given.展开更多
The determination of material formula needs try-and-error experiment,and consumes large amount of time and fund.In order to solve the problem,a comprehensive method is established,via the experiment of artificial-simi...The determination of material formula needs try-and-error experiment,and consumes large amount of time and fund.In order to solve the problem,a comprehensive method is established,via the experiment of artificial-similar material formula of a mine slope.We controlled the samples by the compactness,and arranged the formula of the test group with the method of the uniform formula experiment.The physical and mechanical parameters of these samples were analyzed using the method of the partial least-squares regression(PLS).And a mathematical model of the indexes of physical and mechanics parameters relating to the factors of formulation constituents was established eventually.We used the model to analyze the effect of each formulation constituent on physical and mechanics parameters of samples.The experiment results and analysis illustrates that1)in the formulation of similar material,the effect of raw materials on the internal friction angleφand cohesion C is opposite;2)The method can highly facilitate the process of the of preparing artificial-similar materials,more economic and effective.展开更多
The aim of this article is to extend the theory of several complex variables to the non-commutative realm. Some basic results,such as the Bochner-Martinelli formula,the existence theorem of the solutions to the non-ho...The aim of this article is to extend the theory of several complex variables to the non-commutative realm. Some basic results,such as the Bochner-Martinelli formula,the existence theorem of the solutions to the non-homogeneous Cauchy-Riemann equations,and the Hartogs theorem,are generalized from complex analysis in several variables to Clifford analysis in several paravector variables. In particular,the Bochner-Martinelli formula in several paravector variables unifies the corresponding formulas in the theory of one complex variable,several complex variables,and several quaternionic variables with suitable modifications.展开更多
<正> Let (X_t) be a semimartingale. We denote by (L_t~α(X)) the local time at a of (X_t). If f is the difference of two convex functions on R, it is well known that f(X) is a semimartingale. The purpose of this...<正> Let (X_t) be a semimartingale. We denote by (L_t~α(X)) the local time at a of (X_t). If f is the difference of two convex functions on R, it is well known that f(X) is a semimartingale. The purpose of this note is to give the change of variables formula for the local times of semimartingales, that is, a formula expressing the local times of f(X) in terms of {L_t~α(X),α∈R}.展开更多
文摘In lhis paper, we study the variable structure control of indefinite-dimensionalcontrol systems with the functional analysis method. The reaching conditions, stabilityconditions and the approximating conditions of sliding mode, as well as the generalform of the variable structure control law are given. and the elementary frame of thevariable structure control of indefinite-dimensional systems is built.
基金This work was supported by the Natural Science Foundation of Liaoning Province(2013020022).
文摘A method is proposed to deal with the uncertain multiple attribute group decision making problems,where 2-dimension uncertain linguistic variables(2DULVs)are used as the reliable way for the experts to express their fuzzy subjective evaluation information.Firstly,in order to measure the 2DULVs more accurately,a new method is proposed to compare two 2DULVs,called a score function,while a new function is defined to measure the distance between two 2DULVs.Secondly,two optimization models are established to determine the weight of experts and attributes based on the new distance formula and a weighted average operator is used to determine the comprehensive evaluation value of each alternative.Then,a score function is used to determine the ranking of the alternatives.Finally,the effectiveness of the proposed method is proved by an illustrated example.
文摘In this paper, we obtain an explicit formula of general solution for a class of the homogeneous recurrence of variable coefficients with two indices.
文摘In practice, it is very difficult to find the solution of recurrence relation by using the characteristic roots. By applying iteration and induction we present an explicit formula of general solution for a class of homogeneous trinomial recurrence of variable coefficients with two indices. It provides a concrete and applicable model to solve the relevant problem with computer.
文摘We study the high order equilibrium distributions of a counting random variable. Properties such as moments, the probability generating function, the stop--loss transform and the mean residual lifetime, are derived. Expressions are obtained for higher order equilibrium distribution functions under mixtures and convolutions of a counting distribution. Recursive formulas for higher order equilibrium distribution functions of the (a,b,0) -family of distributions are given.
基金Projects(41372312,51379194)supported by the National Natural Science Foundation of ChinaProject(CUGL140817)supported by the Fundamental Research Funds for the Central Universities of China University of Geosciences(Wuhan)+1 种基金Project(2014CFB894)supported by the Natural Science Foundation of Hubei Province of ChinaProject(2014M552113)supported by the China Postdoctoral Science Foundation
文摘The determination of material formula needs try-and-error experiment,and consumes large amount of time and fund.In order to solve the problem,a comprehensive method is established,via the experiment of artificial-similar material formula of a mine slope.We controlled the samples by the compactness,and arranged the formula of the test group with the method of the uniform formula experiment.The physical and mechanical parameters of these samples were analyzed using the method of the partial least-squares regression(PLS).And a mathematical model of the indexes of physical and mechanics parameters relating to the factors of formulation constituents was established eventually.We used the model to analyze the effect of each formulation constituent on physical and mechanics parameters of samples.The experiment results and analysis illustrates that1)in the formulation of similar material,the effect of raw materials on the internal friction angleφand cohesion C is opposite;2)The method can highly facilitate the process of the of preparing artificial-similar materials,more economic and effective.
基金supported by National Natural Science Foundation of China(Grant No.11371337)Research Fund for the Doctoral Program of Higher Education of China(Grant No.20123402110068)
文摘The aim of this article is to extend the theory of several complex variables to the non-commutative realm. Some basic results,such as the Bochner-Martinelli formula,the existence theorem of the solutions to the non-homogeneous Cauchy-Riemann equations,and the Hartogs theorem,are generalized from complex analysis in several variables to Clifford analysis in several paravector variables. In particular,the Bochner-Martinelli formula in several paravector variables unifies the corresponding formulas in the theory of one complex variable,several complex variables,and several quaternionic variables with suitable modifications.
基金Project supported by the National Natural Science Foundation of China
文摘<正> Let (X_t) be a semimartingale. We denote by (L_t~α(X)) the local time at a of (X_t). If f is the difference of two convex functions on R, it is well known that f(X) is a semimartingale. The purpose of this note is to give the change of variables formula for the local times of semimartingales, that is, a formula expressing the local times of f(X) in terms of {L_t~α(X),α∈R}.
